12 problems

Let the uplink and downlink channel matrices be random variables in a frequency-division duplexing system, and distinguish their channel distributions from their instantaneous real…

The one-dimensional logistic map is … with parameter values in the chaotic regime including $\lambda=3.57,\ldots,4$, and its iterates define a sequence by $x_i=f_\lambda(x_{i-1})$.…

The VAE-LE estimates the channel as $\hat{\boldsymbol{h}}_\text{VAE}$, the true channel as $\boldsymbol{h}$, and its estimation error saturates at…

Let $\rho(d)$ and $\overline{\rho}(d)$ denote the residuals associated with the oracle estimator and practical compressed-sensing schemes, respectively, and let $\hat{L}/L$ measure…

Coherence-band gradient similarity conjecture. For sufficiently large $\eta$, if $j\in B_{\eta}(i)$ and $x_i=x_j$, then

Let $\nu_{OMP}^2$ denote the OMP channel-estimation error, let $N$ be the OFDM size, let $\sigma^2$ be the noise variance, and let $\hat{L}$ be the number of iterations selected by…

Computational-hardness conjecture. In those more difficult combinations of measurement and sparsity rates, no other polynomial-time method will yield accurate estimates of…

Maximal-subset-property conjecture. If $k$ is slightly larger than $n$, then with high probability the only optima of the optimization problem are

Vertex-optimum conjecture. For general $n$, when $k$ is slightly larger than $n$, all non-singular vertices are global optima and solutions to the channel-estimation problem; conse…

Let $\mathbf{B}_L$ and $\mathbf{B}_H$ be the low- and high-frequency basis matrices, respectively, used to model the temporal variation of a channel. In particular, $\mathbf{B}_L$…

Let a multiple input multiple output (MIMO) communication system use channel estimators derived by minimizing tight approximations of its error-probability functions. MIMO estimato…

Practical-coding conjecture. Finite $\tau_{0}$ or finite $\sigma_{\theta}^{2}$ are required to obtain accurate channel estimates in the initial stage.